A number of stories this week discussed what I consider to be problems with or misuse of intellectual property, either by claiming copyright, patents, or other property rights.

Exhibit A: "Twenty Percent of Human Genome is Patented, ACLU Battle to Determine Legality"
U.S. patent law says you can't patent "natural phenomena," so how are parts of the human genome patented? Lawyers argued that if you take DNA out of the cell and modify it (a loosely-defined process, apparently), the genes are no longer considered natural. The biotech company Myriad Genome has patented two breast cancer genes using such methods and developed tests to detect the genes. They claim they would not have been able to finance their research without the patents. Sounds okay so far, right? Here's the problem: because of the patents, Myriad has been able to block other companies from developing similar tests, and universities and other research labs can't study the genes. The ACLU and the AMA aren't happy, and I can't imagine all those millions of people who donate money for breast cancer research want their dollars wasted because a patent is preventing research from being done.

While I don't mean to place the importance of a dog puppet alongside breast cancer research, this article claims that Triumph the Insult Comic Dog won't be following Conan O'Brien home from NBC. Due to intellectual property claims, Triumph doesn't belong to Conan, or even his creator/puppeteer Robert Smigel; he belongs to NBC. Will NBC do anything with Triumph in the future? I doubt it. They just don't want to see Triumph on another network making fans happy. And if anybody has figured out how to keep fans from being happy lately, it's NBC.

Exhibit C: "NEA - Who Owns Your Work? Probably Not You."
Many of the best teachers live by Picasso's words: "Good artists copy. Great artists steal." Increasingly, teachers are helping teachers by blogging, tweeting, and posting lesson plans online for free or profit. Unfortunately, according to the Copyright Act of 1976, teacher-created classroom materials are considered "works for hire," and their ownership belongs to the school district. If schools try to enforce this, there is a very real fear that teachers will respond by creating less content for their classrooms. The solution? Have your local teachers association negotiate with the school district to include teacher copyright protections into teacher contracts or collective bargaining agreements.

Exhibit D: "Critical Commons vs. Hitler: Resource for Free/Open Media and Fair Use"
Another participant in the "Downfall/Hitler in the Bunker" meme, Critical Commons uses the format to demonstrate the growing pains of "multimedia scholarship." Life would be easier for the publishing houses if academicians restricted themselves to journals and books, but current digital tools are pushing us all beyond publishing on paper only. As the academic community becomes more accepting of the "digital humanities," universities and publishers are going to have to adjust or risk their current institutional status. If scholars aren't allowed to thrive in a "remix" culture, their work will struggle to find relevancy among an increasingly media-savvy audience.

A new semester has begun and with it comes new readings. For my Assessment in Math and Science class we read two seminal articles in assessment research, including Black and Wiliam's Inside the Black Box (1998). In discussing room for improvement in assessment, the authors state:

"Approaches are used in which pupils are compared with one another, the prime purpose of which seems to them to be competition rather than personal improvement; in consequence, assessment feedback teaches low-achieving pupils that they lack 'ability,' causing them to come to believe they are not able to learn." (p. 142)

For me, I think competition has always been a healthy part of education, but I understand the authors' concern. Some grading practices, such as grading on a curve (using statistical normal curves that assure some students receive high grades and others receive low grades) are by nature competitive. Unfortunately, that kind of competition not only dissuades students from working cooperatively, but it can sabotage good teaching because of the expectation that some students will fail (Krumboltz & Yeh, 1996), and thus must be used with extreme caution.

Black and Wiliam did not specifically mention grading on a curve, which made me wonder how competitive grading was in general, and what the real source of that competition might be. The questions I posed to the class (a weekly requirement on our course message board) were:

Do you think students are subjected to competition by the teacher and their system of assessment, or is competition a natural reaction of students? Can a teacher design and enforce a competition-free system? If so, how?

After numerous responses and further thought, I think competition is so ingrained in who we are as human beings (both in an innate and culturally-driven way) that attempting to eliminate it in education is not only impossible, but it would be misguided and potentially harmful to try. Blaming the competition for those students who don't compete well isn't a particularly helpful tautology. Surely the issues for struggling students go deeper than that, and fixing the problem by eliminating competition isn't an efficient way of handling the problem.

I suggest teachers and schools try to find ways to utilize the benefits of healthy competition in a fair and voluntary way. Students who wish to compete would always have an outlet, and those who don't hopefully wouldn't feel that anything is being forced upon them. Just as competitive sports or other competitive school activities are voluntary and shouldn't be imposed on all students, the competitive aspects of education shouldn't either, unless students choose to participate.

Amazon.com had been recommending Innumeracy to me for many years, but after attending John Allen Paulos' presentation at the NCTM Annual Meeting in 2008 I decided it was time to buy. Unfortunately, just because I buy a book doesn't mean it gets read right away. Still curious and feeling guilty just letting it sit on my shelf, I decided it was worth part of my winter break to tackle this book.

Compared to technology (one of my other favorite subjects), the mathematical universe moves at a snail's pace. So while Innumeracy was written in 1988, almost all of it is still perfectly relevant today. People still misunderstand, avoid, and often fear mathematics, all of which leads to a personal and collective lack of intellectual power. Paulos fills the book with examples and does a nice job balancing the details of the mathematics involved with ease of reading. (A little experience with probability and the fundamental counting principle helps greatly. It sounds harder than it really is.) For example, Paulos presents this problem:

"A man is downtown, he's mugged, and he claims the mugger was a black man. However, when the scene is reenacted many times under comparable lighting conditions by a courte investigating the case, the victim correctly identifies the race of the assailant only about 80 percent of the time. What is the probability his assailant was indeed black?

Many people will of course say that the probability is 80 percent, but the correct answer, given certain reasonable assumptions, is considerably lower. Our assumptions are that approximately 90 percent of the population is white and only 10 percent black, that the downtown area in question typifies this racial composition, that neither race is more likely to mug people, and that the victim is equally likely to make misidentifications in both directions, black for white and white for black. Given these premises, in a hundred muggings occurring under similar circumstances, the victim will on average identify twenty-six of the muggers as black -- 80 percent of the ten who are actually black, or eight, plus 20 percent of the ninety who were white, or eighteen, for a total of twenty-six. Thus, since only eight of the twenty-six identified as black were black, the probability that the victim actually was mugged by a black given that he said he was is only 8/26, or approximately 31 percent!" (pp. 164-165)

Innumeracy is filled with such examples, enough to make me want to go back through the book a second time and turn some into lesson plans. Most of the examples relate to probability and statistics, because that's where innumerate people are hurt the most. Very few of us are hurt on a regular basis by a lack of calculus understanding, but data are everywhere and misinterpretations happen all the time.

My favorite chapter of the book, and the one of most interest to educators, is chapter 4, "Whence Innumeracy?" Paulos relates a story of his own childhood, where he was excited to work out some mathematics on his own, was shot down by his teacher, and then later learned he was right all along. Paulos goes on to criticize teachers and teacher education programs, claiming a lack of mathematical knowledge on the part of teachers deserves part of the blame for innumeracy. I, like many math teachers, can easily read this as one does about bad drivers: "Sure, there are a lot of bad drivers, but surely I'm not one of them." (Fortunately, I have some test scores that speak for my mathematical competency.) The importance of teacher competency and education programs has received more serious criticism as of late, but like I said, math moves slow, so it shouldn't be surprising (even if it is disappointing) to know that some things haven't changed much (or enough) in the 22 years since Innumeracy was first published. Paulos also targets the shortcomings of the learners of mathematics, addressing math anxiety and a lack of curiosity. Here's the most critical paragraph:

"Different from and much harder to deal with than math anxiety is the extreme intellectual lethargy which affects a small but growing number of students, who seem to be so lacking in mental discipline or motivation that nothing can get through to them. Obsessive-compulsive sorts can be loosened up and people suffering from math anxiety can be taught ways to allay their fears, but what about students who don't care enough to focus any of their energy on intellectual matters? You remonstrate: 'The answer's not X but Y. You forgot to take account of this or that.' And the response is a blank stare or a flat 'Oh, yeah.' Their problems are an order of magnitude more serious than math anxiety." (p. 120)

If you're a math teacher, you know that stare, or that response. It never says, "I understand." It usually says, "Go away," and for some students it's an automatic response, whether they want to understand or not. Fortunately, since 1988 a great deal of work has been done in math education to keep students more engaged with mathematical tasks.

Paulos followed up Innumeracy with a second book, Beyond Numeracy, which I also own but haven't yet read. He's also written a number of other books which are also occupying my shelves, and I hope to get to them all, although, with a semester starting in another week, it might have to wait until another break.